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Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep gradients. The solutions to singularly perturbed…
Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy…
We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…
We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and…
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…
In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…
Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…
In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D…
Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…
The convergence of Boltzmann Fokker Planck solution can become arbitrarily slow with iterative procedures like source iteration. This paper derives and investigates a nonlinear diffusion acceleration scheme for the solution of the Boltzmann…
Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a…
Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…
The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the…
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue problem is reformulated as a fixed point problem of the…
Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…
In recent years, large-scale pre-trained diffusion models have demonstrated their outstanding capabilities in image and video generation tasks. However, existing models tend to produce visual objects commonly found in the training dataset,…
Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…